Impedance Measurement with the MSA
Using the S21/Shunt Method
Impedance is often measured with a vector network analyzer (VNA) by measuring reflection (S11) with a bridge, and then calculating the impedance from S11. Scotty’s Modular Spectrum Analyzer (MSA), operating in VNA mode, can also use an alternative method, in which the device under test (DUT) is shunted to ground between two attenuators, with the signal running into one of the attenuators and out of the other. The transmission (S21) of the test fixture is measured, and impedance is calculated from that S21.
To perform a measurement, a line calibration is first performed with no DUT attached. Then the DUT is attached and scanned. The line calibration is the only necessary calibration; the usual OSL calibration used when measuring reflection is not performed.
The technique is described more fully below. We will first present some test results.
TEST RESULTS WITH 50 OHM TEST FIXTURE
Figure 1 shows impedance measurement of a two 100-ohm resistors mounted in parallel on the back of an SMA connector, and attached to the test fixture.
Figure 1—50 ohm resistance
The measurement of the 50-ohm resistance is very accurate to 100 MHz and quite respectable to 200 MHz. The graph also includes measurement of the parallel capacitance. The measured amount is so low as to be virtually meaningless. It may in part represent a measurement error, but is a very small error. Note the erratic and higher capacitance values at low frequency. These are virtually meaningless, as a 2 or 3 pf capacitance in parallel with a 50-ohm resistor has virtually no effect, and is difficult to measure with any accuracy.
Figure 2 shows measurement of a 150-ohm resistor.
Figure 2—150 ohm resistor
Figure 2 shows a measurement error of about 2%, with very good frequency response. This error is very low, considering the minimal amount of calibration that is required for these measurement.
Figure 3—1 KOhm resistor
It is a challenge for a VNA to measure large impedances, but Figure 3 shows that the MSA does a good job, even at 1KOhm.
Now let’s try a crazy value, so see how high an impedance we can measure.
Figure 4—5.1 KOhm resistor
Figure 4 shows that the measurements of 5.1K resistor are in the ballpark, but have significant error and are very erratic. What is going on is that the measurement of S21 has a resolution of 0.01 dB. With high impedances the measured S21 is very close to zero, and the minimum steps of 0.01 dB translate to large impedance steps. The solution is to use a 200 ohm test fixture, rather than the standard 50 ohm fixture. This is discussed later.
Let’s move to the other extreme of low impedances.
Figure 5—5.6 ohm resistor
Figure 5 shows that a 5.6 ohm resistor can be measured fairly accurately up to 100 MHz, and reasonably well up to 200 MHz. We now also see some series inductance. It is possible this represents measurement error, but it is also possible that it represents true inductance of the resistor. This same inductance may be present with the larger resistors, but represents such a small impedance that is not detected in the presence of the larger resistances. The rising slope of the resistance line, however, suggests there may be some other problems as well. It turns out that the connector from the fixture to the DUT causes some distortions that are not fully accounted for in this minimal-calibration method (remember, we are not doing OSL calibration here).We can show this by directly soldering the resistor onto the test fixture board.
With the 5.6 ohm resistor directly soldered to the test fixture, we get the results shown in Figure 5A.
Figure 5A—5.6 ohm resistor directly soldered to test fixture
Figure 5A shows extremely good results. This indicates that the error in Figure 5 is due to test fixture parasitics, including those of the connector, and are not due to any inherent MSA problem. For these low impedances, we can get good results with the direct-solder method. This also suggests that if we used full OSL calibration with the connectorized fixture, we would get very good results, because OSL should be very effective against test board parasitics.
Let’s push to even lower impedances. Figures 6 and 6A show a 1 ohm resistor, in the first case attached via a connector and in the second directly soldered to the fixture.
Figure 6—1 ohm resistor attached to DUT connector
Figure 6A—1 ohm resistor directly soldered to test fixture
The 1 ohm measurement in Figure 6 is very good at lower frequencies, but gradually deteriorates. Whether it is accurate enough depends on what you are doing. The measurement in Figure 6A is extremely accurate for the full frequency range as far as resistance, and the inductance is stable enough, and close enough to that for the 5.6 ohm resistor, to suggest that it may very well represent the true inductance of the resistor body.
The next lower resistor I have is zero ohms, also known as a direct short. The results are shown in Figures 7 and 7A.
Figure 7—Shorting strip attached to connector
Figure 7A—Shorting strip soldered on the test fixture
Figure 7, using the connector, shows the same upward drift of resistance seen in the previous few images. The inductance in Figure 7 is slightly negative, but is essentially zero. If we were to use OSL calibration for the low impedance values, the Short calibration would essentially correct for the upward resistance drift, and make minimal adjustment to the measured inductance. This would make Figures 5 and 6 look much like Figures 5A and 6A, respectively.
The 420 pH of inductance shown in Figure 7A (the direct-soldered short) is a plausible value for the brass strip, as is the near-zero resistance. We certainly can’t count on high accuracy for such tiny impedances, but the fact that they are plausible and relatively stable values is very encouraging. Again, the measurement by the direct-solder method is excellent.
TEST RESULTS WITH 200 OHM TEST FIXTURE
It was mentioned above that the 5.1K resistor could be better measured in a test fixture that presented 200 ohms to the DUT. The next several images show tests using such a fixture.
Figure 8—5.1 KOhm resistor in 200 ohm test fixture
The measurements in Figure 8 are still not as good as one can obtain with smaller impedances, but they still represent better than 10% accuracy except at the very high frequencies. For such high impedance, this accuracy is excellent for a VNA. And remember, we are still doing this without OSL calibration.
If we need to use a special test fixture for very high impedances, it would be nice if it also worked well at lower impedances, so here are a couple of additional measurements.
Figure 9—1 KOhm resistor in 200 ohm test fixture
Figure 9 shows that the 200 ohm test fixture gives extremely good results for a 1K resistor—2% accuracy to somewhere past 100 MHz.
Figure 10—50 ohm resistor in 200 ohm test fixture
Figure 10 shows that the 200 ohm fixture does a decent job of measuring a 50 ohm resistor, but degenerates a bit at the higher frequencies. The standard 50 ohm fixture did a better job. I also tested a 5.6 ohm resistor, which showed even worse degeneration over frequency, though it was quite good to 50 MHz. My guess is that both the 50 and 5.6 ohm resistors would have given good results if directly soldered to the 200 ohm fixture, or if full OSL calibration were used.
CONCLUSIONS FROM TEST RESULTS
We can conclude that the S21 method of measuring impedance with a connectorized shunt test fixture, using only the normal Line Calibration used for transmission measurements, can provide very nice results from fairly high impedances down to impedances as low as one ohm. However, at low impedances, such as 5.6 ohms, the accuracy begins to deteriorate at lower and lower frequencies, due to the need to better compensate for characteristics of the DUT-Fixture connection. For frequencies above 60 MHz, results can be improved by soldering the DUT directly to the test fixture, if that is feasible, and it is likely that similar improvement could be obtained at low impedances by using OSL calibration.
THE TEST SETUP
Figure 11 shows the general test setup for making impedance measurements using the S21 method in the Shunt configuration.
Figure 11—Test Setup with Shunt Fixture
These tests were performed using the MSA with a buffer amplifier on both the TG output and the MSA input. I used my Active Bridges for the amplifiers. They were functioning simply as amplifiers, not as reflection bridges. The purpose of these amplifiers is to improve the return loss seen by the DUT. The same result could be obtained by using larger attenuators on the fixture, though this would reduce the signal level considerably. I actually also had a 10 dB attenuator on the MSA input, which I always leave in place.
The attenuators and DUT connection were contained on a single small board. The schematic for the 50 ohm fixture is shown in Figure 12.
Figure 12—Schematic of 50 Ohm Test Fixture
Resistors are 0.1%
The attenuators in Figure 12 are standard 50 ohm 7.7 dB attenuators. But note that such attenuators are intended to connect to 50 ohm sources and loads. In this case, the end of the attenuators attached to the DUT see the impedance of the DUT in parallel with the other attenuator. For any DUT other than an open circuit, each attenuator thus sees an impedance smaller than 50 ohms. This causes its attenuation and return loss to differ from what might be expected. As long as the source and load have good return loss, the degradation of the attenuator return loss (as seen from the outside) is not a problem. However, it is possible to improve the test fixture so low impedance DUTs do not disrupt the return loss as much. Figure 13 shows such a fixture.
Figure 13—Improved 50 ohm test fixture.
The return loss seen from the source or load is never worse than 24 dB,
no matter what the DUT impedance.
The two middle resistors in Figure 13 may seem odd, but they are the equivalent of two parallel resistors of 100.5 ohms each. Such resistors would normally be at the inside end of each attenuator, but that is a non-standard 0.1% value.
The most important thing in either test fixture is that the DUT itself see a 50 ohm impedance from each attenuator (meaning it actually sees a net 25 ohms). With these fixtures, if the source and load have return loss of at least 30 dB, the impedance seen by the DUT will be good. The buffer amplifiers in Figure 11 show extremely good return loss, so the main issue is the cabling connecting the amplifiers to the test fixture. We could actually use fairly long quality cables for the connection without any problem.
The schematic of the 200 ohm test fixture is shown in Figure 14.
Figure 14—200 Ohm Test Fixture
The DUT sees exactly 200 ohms on each side; the source
and load see approximately 50 ohms
THE TEST PROCEDURE
To perform impedance measurements using the S21/Shunt method:
This will produce a scan of the DUT impedance. If the scan shows positive inductance, it makes the most sense to graph series inductance and series resistance. If the scan shows positive capacitance, it makes the most sense to graph parallel capacitance and parallel resistance.
The mathematics behind the impedance measurement is very simple. Given the S21 measurement of the test fixture, the impedance of the DUT is:
ZDUT= (R0/2) * S21 / (1-S21)
R0 is the characteristic impedance of the test fixture, either 50 or 200 ohms. S21 must be converted to real, imaginary form to perform this calculation.
This calculation is made automatically by the MSA when you specify that you want to graph impedance, or any impedance-related item (such as RLC values or reflection).
There is one other mathematical step that is a bit more complex. For maximum accuracy, the MSA will compensate for the distortions caused by the length of the connection between the DUT and the test fixture. This requires backing that length out of the Open calibration, and also unwinding the impedance transformation of the DUT that is caused by the presence of that length of transmission line.